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Mathematical Physics

Title:Gauss-Vanicek Spectral Analysis of the Sepkoski Compendium: No New Life Cycles

Abstract: New periods can emerge from data as a byproduct of incorrect processing or
even the method applied. In one such recent instance, a new life cycle with a
62+-3 Myr period was reportedly found (about trend) in genus variations from
the Sepkoski compendium, the world most complete fossil record. The approach
that led to reporting this period was based on Fourier method of spectral
analysis. I show here that no such period is found when the original data set
is considered rigorously and processed in the Gauss-Vanicek spectral analysis.
I also demonstrate that data altering can boost spectral power up to a nearly
100 percent increase in the signal range, thus introducing artificial, "99
percent significant" periods as seen in the corresponding variance-spectra of
noise. Besides geology and paleontology, virtually all science and engineering
disciplines could benefit from the approach described here. The main general
advantages of the Gauss-Vanicek spectral analysis lay in period detection from
gapped records and in straightforward testing of statistical null hypothesis.
The main advantage of the method for physical sciences is its use as a field
descriptor for accurate simultaneous detection of eigenfrequencies and relative
dynamics. Besides analyzing incomplete records, researchers might also want to
remove less-trustworthy data from any time series before analyzing it with the
Gauss-Vanicek method. This could increase both the accuracy and reliability of
spectral analyses in general.

Comments:

Of interest to all sciences. Added a letter containing Errata for a figure discolored due to journal error